As a sphere growing from a point at present in both forward and backward time. The "cone" with a 3-D cross section is now a 4-D object, and you can't embed it in 3-space. That's why we do the 2-D cross section in diagrams.

As we can project the an 3D image on a sheet of paper, can we project a 4D object to the 3D world, not atleast to a sheet of paper. I have heard that George Gamow gave some notes about that in his book 1,2,3 infinity